#textbook #hookslaw #physics #claculation

Pg:- 92 to 96

ch:- 5

Hooke's Law describes the relationship between the force applied to a spring (or any elastic object) and the resulting deformation (stretch or compression) of the spring. It is a fundamental principle in mechanics and is particularly important in the study of elasticity. The law is mathematically expressed as:

F=−kxF

where:

• F is the force applied to the spring (in newtons, N).

• x is the displacement of the spring from its equilibrium (rest) position (in meters, m). This can be either a stretch or a compression.

• k is the spring constant (in newtons per meter, N/m), which measures the stiffness of the spring. A higher value of k means the spring is stiffer.

• The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement, meaning the spring resists deformation (restoring force).

Explanation of the Terms:

• Elasticity: Hooke's Law applies only to elastic materials, where the material returns to its original shape after the force is removed. For a spring, this means it returns to its rest position after being stretched or compressed.

• Linear Proportionality: The relationship between the force and displacement is linear, which means if you double the force, the displacement doubles, as long as the spring is within its elastic limit. Beyond this limit, the spring may not follow Hooke’s Law, and permanent deformation may occur.

Real-World Example:

If you hang a weight on a spring, the spring will stretch. According to Hooke's Law, the amount of stretch is proportional to the weight (force) you hang. For example, if the spring constant kkk is 50 N/m and you apply a force of 10 N, the spring stretches by:

x=Fk=10 N50 N/m=0.2 mx

Elastic Limit:

Hooke’s Law is valid only when the material behaves elastically, meaning it returns to its original form once the force is removed. If the force applied exceeds a certain limit (the elastic limit or yield point), the material may experience permanent deformation and no longer obey Hooke’s Law.